Understanding Arithmetic Sequences | Formula and Examples

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is often referred to as the common difference.

The general formula for an arithmetic sequence is given by:

a_n = a_1 + (n-1)d

where a_n denotes the nth term of the sequence, a_1 represents the first term, n is the position of the term, and d is the common difference.

For example, let’s consider the arithmetic sequence: 3, 7, 11, 15, 19, …

Here, a_1 = 3 (first term) and d = 4 (common difference). Using the formula, we can find any term in the sequence.

To find the 5th term (a_5), we substitute n = 5 into the formula:

a_5 = 3 + (5-1)4
= 3 + 16
= 19

So, the 5th term of the sequence is 19.

Similarly, we can find the common difference (d) by subtracting any two consecutive terms. In this case:

d = 7 – 3 = 4

It is important to note that in arithmetic sequences, the common difference remains constant, and by knowing any two terms or the first term and the common difference, we can easily find the other terms using the formula.

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